http://www.bahamas-travel.org/january-bahamas-cruise-weather/

What to pack for a Western Caribbean cruise in December-January?
My husband and I are going on a Western Caribbean cruise around New Year’s Eve for our anniversary. What should we pack for the weather there? We will be stopping at the Bahamas, Jamaica, and the Grand Caymans. We have our formal wear for Captain’s Night, but beyond that, I am at a loss.
Carry light layers for casual wear. they weather is usually nice and will range from the high sevnties and can drop to the mid 60s at night. The further south you go the less change you will see in temperatures. The light layers are for the evenings or in case of a cold front. Other than that its like regular summer clothing. The Bahamas is the northern most part of the Caribbean (we technically aren’t in the Caribbean sea, but The Atlantic Ocean) and in December its usually still pretty warm during the day and comfortably cool at night (with the exception of cold fronts) so Jamaica and Grand Caymans should be just beautiful.
Cruise to the Bahamas January 2010